Erik Kusch, PhD Student
Department of Biology
Section for Ecoinformatics & Biodiversity
Center for Biodiversity Dynamics in a Changing World (BIOCHANGE)
Aarhus University
14/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 1
Can now set some very intuitive priors!
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[Study Group] Bayesian Statistics with the Rethinking Material 2
k and p are unidentifiable!
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[Study Group] Bayesian Statistics with the Rethinking Material 3
k and p are unidentifiable!
Replace kp
2
No intuitive prior for Θ!
Intuitive prior for p
Standardise variables
No intuitive prior fork because it is
dependant on measurement units
of weight and height.
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[Study Group] Bayesian Statistics with the Rethinking Material 4
k and p are unidentifiable?!
pairs plot to make sense of posteriors
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[Study Group] Bayesian Statistics with the Rethinking Material 5
“Lots of natural relationships are GLM relationships, on a
specific scale of measurement.”
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[Study Group] Bayesian Statistics with the Rethinking Material 6
What strategies lead to selecting
A(quamarine)?
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[Study Group] Bayesian Statistics with the Rethinking Material 7
Each strategy comes with a
vector of probabilities for each
colour.
Identify the probabilities of producing observation for each strategy using Bayes!
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[Study Group] Bayesian Statistics with the Rethinking Material 8
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[Study Group] Bayesian Statistics with the Rethinking Material 9
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[Study Group] Bayesian Statistics with the Rethinking Material 10
State-Space Model: multiple,
hidden strategies produce our
observations.
When states are discrete
categories, we speak of
Hidden Markov Model (HMM).
GLMs struggle with teasing apart hidden states.
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[Study Group] Bayesian Statistics with the Rethinking Material 11
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[Study Group] Bayesian Statistics with the Rethinking Material 12
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[Study Group] Bayesian Statistics with the Rethinking Material 13
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[Study Group] Bayesian Statistics with the Rethinking Material 14
When developing this model, some parameters can benefit from information
about individual primates, while others may not.
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[Study Group] Bayesian Statistics with the Rethinking Material 15
Growth rate might be different for
different individuals/species.
Scaling parameter φ is a physical
feature, not an individual one.
GLMs don’t allow for model
parameters to vary differently for
observational units.
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[Study Group] Bayesian Statistics with the Rethinking Material 16
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[Study Group] Bayesian Statistics with the Rethinking Material 17
Autoregressive model.
Lags farther than one period
back make causal sense.
Measurement error is
propagated.
What we want is a
State-Space Model.
Usually lack any sensible
interpretation of parameters.
14/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 18
Ordinary differential equations.
Lotka-Volterra Model.
Solve through simulation!
No explicit solution for H
t
and L
t
.
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[Study Group] Bayesian Statistics with the Rethinking Material 19
Need to model population dynamics as well
as measurement error.
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[Study Group] Bayesian Statistics with the Rethinking Material 20
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[Study Group] Bayesian Statistics with the Rethinking Material 21
Modelling time-series without
measurement error induces bias.
Reporting uncertainties is the key to honest science.
DISCUSS!
